The cocyclic Hadamard matrices of order less than 40

Ó Catháin, Padraig and Roder, Marc (2011) The cocyclic Hadamard matrices of order less than 40. Designs, Codes, and Cryptography, 58 1: 73-88. doi:10.1007/s10623-010-9385-9


Author Ó Catháin, Padraig
Roder, Marc
Title The cocyclic Hadamard matrices of order less than 40
Journal name Designs, Codes, and Cryptography   Check publisher's open access policy
ISSN 0925-1022
1573-7586
Publication date 2011-01-01
Sub-type Article (original research)
DOI 10.1007/s10623-010-9385-9
Volume 58
Issue 1
Start page 73
End page 88
Total pages 16
Place of publication New York, United States
Publisher Springer New York
Language eng
Formatted abstract
In this paper all cocyclic Hadamard matrices of order less than 40 are classified. That is, all such Hadamard matrices are explicitly constructed, up to Hadamard equivalence. This represents a significant extension and completion of work by de Launey and Ito. The theory of cocyclic development is discussed, and an algorithm for determining whether a given Hadamard matrix is cocyclic is described. Since all Hadamard matrices of order at most 28 have been classified, this algorithm suffices to classify cocyclic Hadamard matrices of order at most 28. Not even the total numbers of Hadamard matrices of orders 32 and 36 are known. Thus we use a different method to construct all cocyclic Hadamard matrices at these orders. A result of de Launey, Flannery and Horadam on the relationship between cocyclic Hadamard matrices and relative difference sets is used in the classification of cocyclic Hadamard matrices of orders 32 and 36. This is achieved through a complete enumeration and construction of (4t, 2, 4t, 2t)-relative difference sets in the groups of orders 64 and 72.
Keyword Classification of Hadamard matrices
Cocyclic Hadamard matrices
Relative difference sets
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
Versions
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 8 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 9 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Wed, 06 Nov 2013, 22:05:55 EST by Kay Mackie on behalf of Mathematics